The GPL licenses are the most common open source licenses and generally the most problematic for companies developing software. SaaS companies are more free to use GPL licensed-code because the obligations of the GPL are triggered upon software distribution and SaaS software by nature is not distributed. (This is often referred to as the GPL "SaaS loophole.")
However, SaaS companies still need to be concerned about software licensing. First, there are a number of licenses, most notably the AGPL, that are (according to the AGPL preamble) “specifically designed to ensure cooperation with the community in the case of network server software.” In essence, the obligation to make source code available is triggered not just by distribution but also by allowing use over a network. These licenses are much less common than the GPL, but are still out there and are designed to plug what has been considered the SaaS loophole in the GPL.
The other “license type” that SaaS companies should watch out for is no license. In the vast majority of audits we perform, we find code that has been appropriated from the internet, but with no clear license. The default of copyright law is that if it’s not your software and you don’t have permission (i.e., a license) you don’t have the right to use it. Therefore, there is risk in doing so.